How can I scale bezier points without curve anchors being affected?
This is because the points handles type is set to Automatic by default. You can try convert them to Free before you scale it.
To do so, in Edit Mode of any Curve object :


Select the points you want to scale
Hit V (or menu: Curve > Control Points > Set Handle Type) and choose Free. The handles change color.
you can now scale points the way you want, constraining them or not, and the handles won't scale accordingly. They will keep their original alignment.
Beware to don't change their type again to Automatic, because it will re-scale them according to their point's new position.